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At least 91 records · Page 5

Generalizing the Gurson model using symbolic regression and transfer learning to relax inherent assumptions

Abstract To generate material models with fewer limiting assumptions while maintaining closed-form, interpretable solutions, we propose using genetic programming based symbolic regression (GPSR), a machine learning (ML) approach that describes data using free-form symbolic expressions. To maximize interpretability, we start from an analytical, derived material model, the Gurson model for porous ductile metals, and systematically relax inherent assumptions made in its derivation to understand each assumption’s contribution to the GPSR model forms. We incorporate transfer learning methods into the GPSR training process to increase GPSR efficiency and generate models that abide by known mechanics of the system. The results show that regularizing the GPSR fitness function is critical for generating physically valid models and illustrate how GPSR allows a high level of interpretability compared with other ML approaches. The method of systematic assumption relaxation allows the generation of models that address limiting assumptions found in the Gurson model, and the symbolic forms allow conjecture of decreased material strength due to void interaction and non-symmetric void shapes.

36 MATERIALS SCIENCE↗

Solution adaptivity using a triangular mesh

Solution adaptivity is discussed first from a general perspective and then from the specific viewpoint of triangular meshes. The use of a general connectivity triangular mesh is emphasized. The development of monitor surfaces and their geometric properties is discussed. Mesh point movement is addressed, as is the dynamic restructuring of the connectivity pattern among moving modes. Changes in the number of mesh nodes to obtain suitable refinement for a physical simulation is examined, and the use of locally regular structures to offset the data structure limitation of a general connectivity triangular mesh and thus to obtain an enhanced range of application is considered. To illustrate the basic features of the adaptive triangular mesh strategy, an application to the study of plasma equilibrium is briefly considered.

Eiseman, P. R.↗

PolyODENet

Kinetics of a reaction network that follows mass-action rate laws can be described with a system of ordinary differential equations (ODEs) with polynomial right-hand side. However, it is challenging to derive such kinetic differential equations from transient kinetic data without knowing the reaction network, especially when the data are incomplete due to experimental limitations. We introduce a program, PolyODENet, toward this goal. Based on the machine-learning method Neural ODE, PolyODENet defines a generative model and predicts concentrations at arbitrary time. As such, it is possible to include unmeasurable intermediate species in the kinetic equations. Importantly, we have implemented various measures to apply physical constraints and chemical knowledge in the training to regularize the solution space.

Wu, Qin [Brookhaven National Lab. (BNL), Upton, NY↗

One-loop matching for quark dipole operators in a gradient-flow scheme

The quark chromoelectric dipole (qCEDM) operator is a CP-violating operator describing, at hadronic energies, beyond-the-standard-model contributions to the electric dipole moment of particles with nonzero spin. In this paper we define renormalized dipole operators in a regularization-independent scheme using the gradient flow, and we perform the matching at one loop in perturbation theory to renormalized operators of the same and lower dimension in the more familiar MS scheme. We also determine the matching coefficients for the quark chromo-magnetic dipole operator (qCMDM), which contributes for example to matrix elements relevant to CP-violating and CP-conserving kaon decays. The calculation provides a basis for future lattice QCD computations of hadronic matrix elements of the qCEDM and qCMDM operators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Interpolating Fields of Carbon Monoxide Data Using a Hybrid Statistical-Physical Model

Atmospheric Carbon Monoxide (CO) is a pollutant gas of which the US congress has mandated regular monitoring, and satellite sensors can be used to retrieve regional concentrations of CO over several vertical layers. However, CO at cloudy locations cannot be observed and have to be estimated from the observed data set, resulting in an interpolation problem. The current state-of-the-art solution is to combine prior information, computed by a deterministic physical model, with observations. However, the deterministic model may introduce uncertainties that do not derive from the data. While sharing certain features with the physical model, this paper presents a Bayesian hierarchical model for interpolating CO on a 3-dimensional spatial grid, across time. To our knowledge such a model has not been considered before. The model is applied to a hypothetical air-quality monitoring scenario, and is compared to existing interpolation methods. The results provide motivation for the use of the statistical model for regional to local applications.

Arellano, A. A.↗

A gradient-based deep neural network model for simulating multiphase flow in porous media

We report simulation of multiphase flow in porous media is crucial for the effective management of subsurface energy and environment-related activities. The numerical simulators used for modeling such processes rely on spatial and temporal discretization of the governing mass and energy balance partial-differential equations (PDEs) into algebraic systems via finite-difference/volume/element methods. These simulators usually require dedicated software development and maintenance, and suffer low efficiency from a runtime and memory standpoint for problems with multi-scale heterogeneity, coupled-physics processes or fluids with complex phase behavior. Therefore, developing cost-effective, data-driven models can become a practical choice, and in this work, we choose deep learning approaches as they can handle high dimensional data and accurately predict state variables with strong nonlinearity. In this paper, we describe a gradient-based deep neural network (GDNN) constrained by the physics related to multiphase flow in porous media. We tackle the nonlinearity of flow in porous media induced by rock heterogeneity, fluid properties, and fluid-rock interactions by decomposing the nonlinear PDEs into a dictionary of elementary differential operators. We use a combination of operators to handle rock spatial heterogeneity and fluid flow by advection. Since the augmented differential operators are inherently related to the physics of fluid flow, we treat them as first principles prior knowledge to regularize the GDNN training. We use the example of pressure management at geologic CO 2 storage sites, where CO 2 is injected in saline aquifers and brine is produced, and apply GDNN to construct a predictive model that is trained with physics-based simulation data and emulates the physics process. We demonstrate that GDNN can effectively predict the nonlinear patterns of subsurface responses, including the temporal and spatial evolution of the pressure and saturation plumes. We also successfully extend the GDNN to convolutional neural network (CNN), namely gradient-based CNN (GCNN), and validate its capability to improve the prediction accuracy. GDNN has great potential to tackle challenging problems that are governed by highly nonlinear physics and enable the development of data-driven models with higher fidelity.

42 ENGINEERING↗

Repartitioning the Hamiltonian in many-body second-order Brillouin–Wigner perturbation theory: Uncovering new size-consistent models

Second-order Møller-Plesset perturbation theory is well-known as a computationally inexpensive approach to the electron correlation problem that is size-consistent with a size-consistent reference but fails to be regular. On the other hand, the less well-known many-body version of Brillouin-Wigner perturbation theory has the reverse properties: it is regular but fails to be size-consistent when used with the standard MP partitioning. Consequently, its widespread use remains limited. In this work, we analyze the ways in which it is possible to use alternative non-MP partitions of the Hamiltonian to yield variants of BW2 that are size-consistent as well as regular. We show that there is a vast space of such BW2 theories and also show that it is possible to define a repartitioned BW2 theory from the ground state density alone, which regenerates the exact correlation energy. We also provide a general recipe for deriving regular, size-consistent, and size-extensive partitions from physically meaningful components, and we apply the result to small model systems. The scope of these results appears to further set the stage for a revival of BW2 in quantum chemistry.

Ab initio perturbation↗

Physics-assisted generative adversarial network for X-ray tomography

X-ray tomography is capable of imaging the interior of objects in three dimensions non-invasively, with applications in biomedical imaging, materials science, electronic inspection, and other fields. The reconstruction process can be an ill-conditioned inverse problem, requiring regularization to obtain satisfactory results. Recently, deep learning has been adopted for tomographic reconstruction. Unlike iterative algorithms which require a distribution that is known a priori , deep reconstruction networks can learn a prior distribution through sampling the training distributions. In this work, we develop a Physics-assisted Generative Adversarial Network (PGAN), a two-step algorithm for tomographic reconstruction. In contrast to previous efforts, our PGAN utilizes maximum-likelihood estimates derived from the measurements to regularize the reconstruction with both known physics and the learned prior. Compared with methods with less physics assisting in training, PGAN can reduce the photon requirement with limited projection angles to achieve a given error rate. The advantages of using a physics-assisted learned prior in X-ray tomography may further enable low-photon nanoscale imaging.

47 OTHER INSTRUMENTATION↗

Overview and Scientific Agenda of Global Precipitation Mission

This paper addresses the status of the Global Precipitation Mission (GPM) currently planned for launch in the 2007-2008 time frame. The GPM notional design involves a 9-member satellite constellation, one of which wilt be an advanced TRMM-like "core" satellite carrying a dual-frequency Ku-Ka band radar (DFPR) and a TMI-like radiometer. The other eight members of the constellation will be considered daughters of the core satellite, each carrying some type of passive microwave radiometer measuring across the 10.7 - 85 GHz ,frequency range - likely to include a combination of lightweight satellites and co-existing operational/Experimental satellites carrying passive microwave radiometers (i.e., SSM/I and AMSR-E & -F). The constellation is designed to provide no worse than 3-hour sampling at any spot on the globe using sun-synchronous orbit architecture for the daughter satellites, with the core satellite providing relevant measurements on internal cloud-precipitation microphysical processes and the "training-calibrating" information for retrieval algorithms used on daughter satellite measurements. The GPM is organized internationally, currently involving a partnership between NASA in the US, NASDA in Japan, and ESA in Europe (representing the European community nations). The mission is expected to involve additional international participants, sister agencies to the mainstream space agencies, and a diverse collection scientists from academia, government, and the private sector, A critical element in understanding the scientific thinking which has motivated the GPM project is an understanding of what scientific problems TRMM has and has not been able to address and at what scales. The TRMM satellite broke important scientific ground because it carried to space an array of rain-sensitive instruments, two of which were specifically designed for physical precipitation retrieval. These were the 9-channel TRMM Microwave Imager (TMI) and the 13.8 GHz Precipitation Radar (PR). By the same token, because TRMM is a single satellite in a low inclination, low altitude, non-sun-synchronous orbit, it cannot provide global coverage or regular diurnal sampling. These features are essential for many current scientific inquiries involving physical processes of climate and the global water cycle, the modeling of hydrometeorological-biogeochemical cycling, and coupled land-atmosphere/ocean-atmosphere exchanges. Moreover, TRMM has not been able to retrieve explicit properties of the drop size distribution (DSD), a final major barrier to making accurate rain measurements, because the single frequency TRMM radar cannot measure differential reflectivity. which is a minimal requirement for attacking rain retrieval within the framework of extinction cross-section-dependency. GPM is expected to surmount much of the DSD retrieval problem because its core satellite wilt have the capacity to make differential reflectivity measurements with its Ku-Ka band radar (13.6 - 35 GHz) called DFPR - being developed by NASDA/CRL in Japan. This paper will provide an overview of the above issues as well as present a discussion on the expected measurement improvements.

Smith, Eric A.↗

Distributed Resilience in High-Energy Physics Data Acquisition

Historical experience in the High-Performance Computing community teaches us that as computing systems grow, the instance of failures goes from rare to a regular occurrence. A survey of the growth in the size and complexity of Data AcQuisition (DAQ) networks in High-Energy Physics (HEP) experiments reveals that these networks are scaling exponentially, trending to a point where automated fault handling should be considered over the current manual practice, especially given the rarity of data such as in DUNE's mission to observe core-collapse supernovae. We propose a general system, DiDAQt, which is designed to provide fault detection and handling in HEP DAQs specifically, through MPI-like primitives that allow it to be added easily to existing systems. We evaluate the scalability and response time of a prototype on the FABRIC national testbed, with results indicating sufficient scalability for current and near-future DAQs as well as practical response times (under 1 microsecond decision time).

Wolosewicz, A. [IIT, Chicago]↗

Transient phenomena in the axion assisted Schwinger effect

Particle production induced by a time-dependent background is well understood as the projection of the time-evolved initial state onto a set of final states. While the asymptotic initial and final states are well defined in the usual way, the definition of particles and antiparticles at intermediate times in the presence of external fields is ambiguous. These external fields moreover induce divergences which require regularization. In this paper we clarify some subtleties in the computation of transient effects in physical quantities for fermions in a homogeneous axion background, including Schwinger production in background electromagnetic fields. The presence of the axion requires particular care as well as knowledge of the UV theory when regulating the theory and computing the vacuum contribution to the fermion energy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

3-regular three-XORSAT planted solutions benchmark of classical and quantum heuristic optimizers

With current semiconductor technology reaching its physical limits, special-purpose hardware has emerged as an option to tackle specific computing-intensive challenges. Optimization in the form of solving quadratic unconstrained binary optimization problems, or equivalently Ising spin glasses, has been the focus of several new dedicated hardware platforms. These platforms come in many different flavors, from highly-efficient hardware implementations on digital-logic of established algorithms to proposals of analog hardware implementing new algorithms. In this work, we use a mapping of a specific class of linear equations whose solutions can be found efficiently, to a hard constraint satisfaction problem (three-regular three-XORSAT, or an Ising spin glass) with a 'golf-course' shaped energy landscape, to benchmark several of these different approaches. We perform a scaling and prefactor analysis of the performance of Fujitsu's digital annealer unit (DAU), the D-Wave advantage quantum annealer, a virtual MemComputing machine, Toshiba's simulated bifurcation machine (SBM), the SATonGPU algorithm from Bernaschi et al, and our implementation of parallel tempering. We identify the SATonGPU and DAU as currently having the smallest scaling exponent for this benchmark, with SATonGPU having a small scaling advantage and in addition having by far the smallest prefactor thanks to its use of massive parallelism. Furthermore, our work provides an objective assessment and a snapshot of the promise and limitations of dedicated optimization hardware relative to a particular class of optimization problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Deep learning-enabled probing of irradiation-induced defects in time-series micrographs

Modeling time-series data with convolutional neural networks (CNNs) requires building a model to learn in batches as opposed to training sequentially. Coupling CNNs with in situ or operando techniques opens the possibility of accurately segmenting dynamic reactions and mass transport phenomena to understand how materials behave under the conditions in which they are used. In this article, in situ ion irradiation transmission electron microscopy (TEM) images are used as inputs into the CNN to assess the defect generation rate, defect cluster density, and saturation of defects. We then use the output segmentation maps to correlate with conventional TEM micrographs to assess the model’s ability to detail nanoscale interactions. Next, we discuss the implications of preprocessing and hyperparameters on model variability, accuracy when expanded to other datasets, and the role of regularization when controlling model variance. Ultimately, we eliminate human bias when extrapolating physical metrics, speed up analysis time, decouple reactions that happen at 100 ms intervals, and deploy models that are both accurate and transferable to similar experiments.

Burns, Kory (ORCID:0000000158019909)↗

Error Propagation in Microwave Soil Moisture and Vegetation Optical Depth Retrievals

Satellite soil moisture and vegetation optical depth (VOD; related to the total vegetation water mass per unit area) are increasingly being used to study water relations in the soil-plant continuum across the globe. However, soil moisture and VOD are typically jointly estimated, where errors in the optimization approach can cause compensation between both variables and confound such studies. It is thus critical to quantify how satellite microwave measurement errors propagate into soil moisture and VOD. Such a study is especially important for VOD given limited investigations of whether VOD reflects in-situ plant physiology. Furthermore, despite new approaches that constrain (or regularize) VOD dynamics to reduce soil moisture errors, there is limited study of whether regularization reduces VOD errors without obscuring true vegetation temporal dynamics. Here, we find that, across the globe, VOD is less robust to measurement error (more difficult for optimization methods to find the true solution) than soil moisture in their joint estimation. However, a moderate degree of regularization (via time-constrained VOD) reduces errors in VOD to a greater degree than soil moisture and reduces spurious soil moisture-VOD coupling. Furthermore, despite constraining VOD time dynamics, regularized VOD variations on sub-weekly scales are both closer to simulated true VOD time series and have global VOD post-rainfall responses with reduced error signatures compared to VOD retrievals without regularization. Ultimately, we recommend moderately regularized VOD for use in large scale studies of soil-plant water relations because it suppresses noise and spurious soil moisture-VOD coupling without removing the physical signal.

Vegetation optical depth↗

Health Assessment and Performance Monitoring of Large Machine Diagnostics

Diagnostic machines are a crucial component of the Stockpile Stewardship Program for data collection, toward the ultimate goal of improving our understanding of nuclear physics. These systems consist of interactions between many complex components, and require regular maintenance for acceptable performance. The Cygnus X-ray diagnostic located at the Nevada National Security Site's U1a underground facility which provides radiographic data for subcritical experiments, is a prime example of these systems. Component degradation and failures within Cygnus can result in system downtime and data loss, affecting schedules and increasing experiment costs. To evade such failures, years worth of data on machine performance has been collected on the two Cygnus axes in the form of voltage and current measurements of Cygnus' various components. Using these as input, we have developed machine learning techniques for assessing the health of Cygnus, with the ultimate goal of predicting declining performance and machine failure.

97 MATHEMATICS AND COMPUTING↗

Inverse problems: Fuzzy representation of uncertainty generates a regularization

In many applied problems (geophysics, medicine, and astronomy) we cannot directly measure the values x(t) of the desired physical quantity x in different moments of time, so we measure some related quantity y(t), and then we try to reconstruct the desired values x(t). This problem is often ill-posed in the sense that two essentially different functions x(t) are consistent with the same measurement results. So, in order to get a reasonable reconstruction, we must have some additional prior information about the desired function x(t). Methods that use this information to choose x(t) from the set of all possible solutions are called regularization methods. In some cases, we know the statistical characteristics both of x(t) and of the measurement errors, so we can apply statistical filtering methods (well-developed since the invention of a Wiener filter). In some situations, we know the properties of the desired process, e.g., we know that the derivative of x(t) is limited by some number delta, etc. In this case, we can apply standard regularization techniques (e.g., Tikhonov's regularization). In many cases, however, we have only uncertain knowledge about the values of x(t), about the rate with which the values of x(t) can change, and about the measurement errors. In these cases, usually one of the existing regularization methods is applied. There exist several heuristics that choose such a method. The problem with these heuristics is that they often lead to choosing different methods, and these methods lead to different functions x(t). Therefore, the results x(t) of applying these heuristic methods are often unreliable. We show that if we use fuzzy logic to describe this uncertainty, then we automatically arrive at a unique regularization method, whose parameters are uniquely determined by the experts knowledge. Although we start with the fuzzy description, but the resulting regularization turns out to be quite crisp.

Kreinovich, V.↗

Recent developments in mathematical aspects of relativistic fluids

Abstract We review some recent developments in mathematical aspects of relativistic fluids. The goal is to provide a quick entry point to some research topics of current interest that is accessible to graduate students and researchers from adjacent fields, as well as to researches working on broader aspects of relativistic fluid dynamics interested in its mathematical formalism. Instead of complete proofs, which can be found in the published literature, here we focus on the proofs’ main ideas and key concepts. After an introduction to the relativistic Euler equations, we cover the following topics: a new wave-transport formulation of the relativistic Euler equations tailored to applications; the problem of shock formation for relativistic Euler; rough (i.e., low-regularity) solutions to the relativistic Euler equations; the relativistic Euler equations with a physical vacuum boundary; relativistic fluids with viscosity. We finish with a discussion of open problems and future directions of research.

Disconzi, Marcelo (ORCID:0000000234497778)↗

Volumetric Rendering on Wavelet-Based Adaptive Grid

Numerical modeling of physical phenomena frequently involves processes across a wide range of spatial and temporal scales. In the last two decades, the advancements in wavelet-based numerical methodologies to solve partial differential equations, combined with the unique properties of wavelet analysis to resolve localized structures of the solution on dynamically adaptive computational meshes, make it feasible to perform large-scale numerical simulations of a variety of physical systems on a dynamically adaptive computational mesh that changes both in space and time. Volumetric visualization of the solution is an essential part of scientific computing, yet the existing volumetric visualization techniques do not take full advantage of multi-resolution wavelet analysis and are not fully tailored for visualization of a compressed solution on the wavelet-based adaptive computational mesh. Our objective is to explore the alternatives for the visualization of time-dependent data on space-time varying adaptive mesh using volume rendering while capitalizing on the available sparse data representation. Two alternative formulations are explored. The first one is based on volumetric ray casting of multi-scale datasets in wavelet space. Rather than working with the wavelets at the finest possible resolution, a partial inverse wavelet transform is performed as a preprocessing step to obtain scaling functions on a uniform grid at a user-prescribed resolution. As a result, a solution in physical space is represented by a superposition of scaling functions on a coarse regular grid and wavelets on an adaptive mesh. An efficient and accurate ray casting algorithm is based just on these coarse scaling functions. Additional details are added during the ray tracing by taking an appropriate number of wavelets into account based on support overlap with the interpolation point, wavelet coefficient magnitude, and other characteristics, such as opacity accumulation (front to back ordering) and deviation from frontal viewing direction. The second approach is based on complementing of wavelet-based adaptive mesh to the traditional Adaptive Mesh Refinement (AMR) mesh. Both algorithms are illustrated and compared to the existing volume visualization software for Rayleigh-Benard thermal convection and electron density data sets in terms of rendering time and visual quality for different data compression of both wavelet-based and AMR adaptive meshes.

Vezolainen, Alexei V.↗